Damek Davis

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math.PR2026

The sharp one-dimensional convex sub-Gaussian comparison constant

Damek Davis, Sam Power

Let $X$ be an integrable real random variable with mean zero and two-sided sub-Gaussian tail $P (∣ X ∣ > t) \leq 2 e^{- t^{2} /2}$ for all $t \geq 0$ . We determine the smallest consta…

math.PR2026

Counting partial Hadamard matrices in the cubic regime

Damek Davis

We give a precise asymptotic formula for the number of $n \times 4 t$ partial Hadamard matrices in the regimes $t / n^{3} \to \infty$ and $t / n^{3} \to I^$ for sufficiently large fixed $I^$ . Th…

math.PR2025

Spectral norm bound for the product of random Fourier-Walsh matrices

Libin Zhu, Damek Davis, Dmitriy Drusvyatskiy +1

We consider matrix products of the form $A_{1} (A_{2} A_{2})^{⊤} \dots (A_{m} A_{m}^{⊤}) A_{m + 1}$ , where $A_{i}$ are normalized random Fourier-Walsh matrices. We identify an interesting polyn…